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Chapter 16: Q79P (page 626)

A metal sphere of radius r1 carries a positive charge of amount Q. A concentric spherical metal shell with inner radius r2 and outer radius r3 surrounds the inner sphere and carries a total positive charge of amount 4Q, with some of this charge on the outer surface (at r3) and some on the inner surface (at r2).(a) How is the charge 4Q distribute on the two surfaces of the outer shell? Prove this! (b) What is the potential (relative to infinity) just outside r3 halfway between r2 and r3 just inside r2, just outside r1 and at the center?

Short Answer

Expert verified

The charge distributed on the inner surface of shell is -Q and charge distributed on the inner surface of shell is 5Q .

Step by step solution

01

Identification of given data

The charge of metal sphere is Q1 = Q.

The radius of metal sphere is r1.

The total positive charge on concentric shell is Q2 + Q3= 4Q

02

Conceptual Explanation

The net charge between metal sphere and inner surface of shell should be zero to maintain the polarity there.

03

Determination of charge distribution of spherical shell on the inner and outer surface of shell

The net charge between metal sphere and inner surface of the shell is zero, so Q1 + Q2 = 0

Here, Q2 is the charge on the inner surface of shell.

Substitute all the values in the above equation.

Q + Q2 = 0

Q2 = - Q

The charge on the outer surface of concentric shell is given as: Q2 + Q3= 4Q

Here, Q3 is the charge on the outer surface of shell.

Substitute all the values in the above equation.

-Q+Q3=4QQ3=5Q

Therefore, the distributed on the inner surface and outer surface of the concentric shell are -Q and Q5 .

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A thin spherical shell of radius \({R_1}\)made of plastic carries a uniformly distributed negative charge \( - {Q_1}\). A thin spherical shell of radius \({R_2}\)made of glass carries a uniformly distributed positive charge \( + {Q_2}\). The distance between centers is \(L\), as shown in Figure 16.80. (a) Find the potential difference \({V_B} - {V_A}\). Location A is at the center of the glass sphere, and location \(B\) is just outside the glass sphere. (b) Find the potential difference \({V_C} - {V_B}\). Location \(B\) is just outside the glass sphere, and location \(C\) is a distance d to the right of \(B\). (c) Suppose the glass shell is replaced by a solid metal sphere with radius R2 carrying charge \( + {Q_2}\). Would the magnitude of the potential difference \({V_B} - {V_A}\) be greater than, less than, or the same as it was with the glass shell in place? Explain briefly, including an appropriate physics diagram.
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